Solve by Gaussian elimination method
4x+2y-5z=13
x+y+z=2
2x-y-3z=3
subtract 4*#2 and 2*#3 from #1, eliminating x.
4x+2y-5z=13
0x-2y-9z = 5
0x+4y+z = 7
Now eliminate y by adding #2 to #1, and 2*#2 to #3.
4x+0y-14z = 18
0x-2y-9z = 5
0x+0y-17z = 17
Now you know z = -1, so
4x+14 = 18 => x=1
-2y+9 = 5 => y=2